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Accurate six-band nearest-neighbor tight-binding model for the π-bands of bulk graphene and graphene nanoribbons
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10.1063/1.3582136
/content/aip/journal/jap/109/10/10.1063/1.3582136
http://aip.metastore.ingenta.com/content/aip/journal/jap/109/10/10.1063/1.3582136

Figures

Image of FIG. 1.
FIG. 1.

(a) Bulk bands of graphene from the DFT + GW calculations used to fit the parameters of Table I. The highlighted area around the K-point is expanded in part (b). (b) the bulk bands of all three models in the vicinity of K: DFT + GW (diamonds), the p/d model (solid lines) and the -only model (dotted lines). The -only model has parameters ; the nonzero onsite term is chosen to align its K -point with that of the other calculations and the common K-point energy is indicated by the heavy dashed horizontal line labeled EK . Note the asymmetry of the DFT + GW and p/d bands about EK in contrast to the exact symmetry of the -only bands about this energy.

Image of FIG. 2.
FIG. 2.

Gaps (a) and bands (b)–(d) of AGNRs; the DFT and p/d model AGNRs are hydrogen passivated while the -only model AGNRs are not, and the uppermost valence band of each model is aligned to facilitate comparison. In panel (a) the DFT gaps are plotted with diamonds, those of the p/d model with open circles, and those of the -only model with squares. Lines, which are guides to the eye, denote families: (dashed), (solid), and (dotted). The hydrogen and H-C parameters of Table I were optimized to the DFT results for only AGNR-7, -8, and -9. All other AGNRs use these same parameters. Note the excellent agreement of the p/d model with DFT and the poor agreement of the -only results.

Image of FIG. 3.
FIG. 3.

Current-voltage characteristics of the AGNR-12 MOSFET of Ref. 14 as calculated with the -only (dotted lines and closed symbols) and p/d models (solid lines and open symbols) for two different drain biases. Computed points are indicated by symbols: circles and squares . Note in Fig. 2(c) the larger AGNR bandgap in the -only model vs the p/d model.

Image of FIG. 4.
FIG. 4.

Differential conductance of a rough AGNR-12 vs line edge roughness probability. Symbols are calculated conductances: Open circles (, N channel), solid circles (, P channel), open diamonds (p/d, N channel), or solid diamonds (p/d, P channel). Each computed point is the average of 250 samples. Note the artificial symmetry of the N- and P-channel AGNRs in the -only model which does not appear in the p/d model.

Image of FIG. 5.
FIG. 5.

Differential conductance of a rough AGNR-13 vs line edge roughness probability; note the logarithmic scale. Symbols are calculated conductances: Open circles (, N channel), solid circles (, P channel), open diamonds (p/d, N channel), or solid diamonds (p/d, P channel). Each computed point is the average of 250 samples. Note the artificial symmetry of the N- and P-channel AGNRs in the -only model which does not appear in the p/d model.

Tables

Generic image for table
Table I.

C-C and H-C onsite and nearest-neighbor tight-binding parameters used in the p/d model; all values are in eV. To simplify the treatment we employ only a single H-C pd nearest-neighbor parameter: .

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/content/aip/journal/jap/109/10/10.1063/1.3582136
2011-05-16
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Accurate six-band nearest-neighbor tight-binding model for the π-bands of bulk graphene and graphene nanoribbons
http://aip.metastore.ingenta.com/content/aip/journal/jap/109/10/10.1063/1.3582136
10.1063/1.3582136
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